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Determine the maximum power of 2 that divides

\[(1+tan 1)(1+tan 2 )(1+tan 3).....(1+tan 42)(1+tan 43)(1+tan 44)\]

DETAILS AND ASSUMPTIONS:

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(1)\( DE || BC \) such that \(A - D - B , A - E - C\)

(2)\( JG || CA \) such that \(B - J - C , B - G - A\)

(3)\( FI || AB \) such that ...

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